The problem of pricing a collateralized loan comes from the realms of traditional finance and stock loans. Associated research on this was pioneered by Xia and Zhou (2007). Under the Black–Scholes model, they derived a closed-form pricing formula for the infinite-maturity stock loan by solving the related optimal stopping problem. Equilibrium adapts the approach proposed by Xia and Zhou, and comes up with an elegant pricing solution that depends on borrower portfolio risk and the level of portfolio collateralization.
We introduce a constant interest rate term, R0 = 1% by default. 20% of R0 goes to validators to fund their operations, while the other 80% goes to the treasury, acting as a final reserve according to our risk model.
We introduce scaling parameter alpha, which equals 0.05 by default. Its main purpose is to reduce the very high interest rate we get from extreme crypto volatility numbers. Assuming the default values for these parameters, here's the approximate interest rate breakdown for a borrower portfolio, given its collateralization ratio and the ratio of dollar liquidity in bailsman and collateral pools.
Further improvements to the pricing model may include adapting the jump diffusion process to model the collateral risk, as well as adapting the model to account for margin calls and LTV requirements. This is subject of our ongoing R&D work.